just saying is a filling phrase which does not have a close correspondent in German
In most cases, just saying is a filling phrase and could well be omitted without hurting the meaning. However, just saying is a pretty common filling phrase in English. For translating it, it is important to understand that it is much more common in English than any of its translations are in German. So, even if there are translations such as
- Ich sag's nur.
- Will ich nur mal gesagt haben.
- Wollte ich nur mal gesagt haben.
- (Nur) Um's mal zu erwähnen.
- Um's mal erwähnt zu haben.
which are even idiomatic in German, you would most probably just omit it in German. That's why I think the closest translation is - as mtwde has already figured - actually
because this is the very normal way of introducing some information which might not be super-relevant, just as by the way in English.
You should try to translate the communicative function
Even if just saying is "just" a filling phrase, it surely has a communicative function. For translating, it is more important to keep this function than to translate the mere words: What are situations when just saying is used, and what is the intention of the speaker using it in that certain situation? Unfortunately my English skills are not good enough to make this analysis for English, but if you would provide such an analysis in your question, we could help you finding idiomatic correspondents for each situation in German.
Using just saying as a means to suggest something
For the context of making a suggestion, a German way of fulfilling this communicative function could be to make it a question:
There is a restaurant nearby. Just saying.
Hast du schon von dem neuen Restaurant um die Ecke gehört?
Schwarzenegger, has a new movie out. Just saying.
Hast du schon den neuen Schwarzenegger-Film gesehen?
I believe German not having such a common filling phrase which corresponds to just saying is the reason, why just saying is used as an anglicism in German, especially amongst younger folks. Here, using the anglicism does not only import the (translatable) words, but also imports the habitualness of the filling phrase from English into German.